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Keywords:
complementarity problem; symmetric cone; Levenberg-Marquardt method; Euclidean Jordan algebra; local error bound
complementarity problem; symmetric cone; Levenberg-Marquardt method; Euclidean Jordan algebra; local error bound
Summary:
In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that the method is stable and efficient.
References:
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